economic io

have 3 questions that are related to Economic–Industrial Organization.
The deadline is April 28, by mid night. (No late work!)
You may need to use the text book: Industrial Organization: Theory and Applications: Oz Shy

Here they are:

Q1:
The inverse demand function for QuasiSmart-Phones is P = 10-Q. Assume that a single …firm initially
operates in this market (…firm 1) and its marginal cost is c = 2. Firm 1 is facing the threat of entry,
since fi…rm 2 is evaluating whether to join the market. There is a …fixed entry cost F > 0 and …firm 2
has the same marginal cost than …rm 1. First, the potential entrant observes …rm 1’s output level and
then it decides whether or not to enter. If fi…rm 2 enters, both fi…rms compete a la Cournot. Find the
range of values of F for which fi…rm 1 (incumbent) decides to accommodate entry. [15 Points]

 

Q2:
Microsoft and Apple produce differentiated goods, Microsoft Surface (MS) and iPad (iP), respectively.
There are two types of buyers in the economy, those who are …rst time buyers (inexperienced consumers)
and those who have purchased the product before (experienced consumers). The group of inexperienced
consumers represents the 45% of the total group of consumers. Assume that the group of experienced
consumers is divided into two subgroups: those who prefer to purchase MS over brand iP, and those
who prefer iP over MS. Let , 0 < β < 1, be the fraction of MS-oriented consumers (among experienced
consumers). Hence, (1β) is the fraction of iP-oriented consumers (among experienced consumers). In
addition, …rms must decide between two advertising methods: Persuasive (P) or Informative advertising(I).

(a) Following Assumption 11.1 (page 292), identify the pro…t level for each …firm and the aggregate
pro…t under all four possible outcome. [8 Points]
(b) Discuss under which conditions both fi…rms will use informative advertising. Discuss your results.
[8 Points]

 

Q3:
Prove the second part of Proposition 12.1 (page 309) using the same procedure as the one used in the
proof of the …rst part. [10 Points]